Forbidden Subgraphs and Forbidden Substructures

Journal of Symbolic Logic 66 (3):1342-1352 (2001)
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Abstract

The problem of the existence of a universal structure omitting a finite set of forbidden substructures is reducible to the corresponding problem in the category of graphs with a vertex coloring by two colors. It is not known whether this problem reduces further to the category of ordinary graphs. It is also not known whether these problems are decidable.

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Ramsey Theory for Countable Binary Homogeneous Structures.Jean A. Larson - 2005 - Notre Dame Journal of Formal Logic 46 (3):335-352.

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